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Whisk the egg yolks together in a heat-proof bowl. Set aside.
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Heat the cream, milk, and sugar together in a heavy-bottomed saucepan.
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Remove mixture just before boiling and slowly pour into the egg yolks whisking constantly.
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Strain the mixture back into the saucepan.
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Heat until it thickens, covering the back of a wooden spoon.
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Pour back into the bowl, cover plastic wrap so the wrap is touching the mixture.
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Refrigerate for 3 hours or overnight.
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Pour the mixture into an ice cream maker.
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Process according to the manufacturer's instructions.
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When ice cream reaches soft serve consistency, stir in the blackberries.
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Transfer to a freezer-proof container.
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Place in the freezer for a few hours or until ready to serve.